Difference between revisions of "User:Boris Tsirelson/sandbox2"
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Mysterious. | Mysterious. | ||
| + | |||
| + | ==Sinusoidal spiral== | ||
| + | |||
| + | <center><asy> | ||
| + | import graph; | ||
| + | size (200); | ||
| + | |||
| + | real r = 2.3; | ||
| + | real m = 4; | ||
| + | |||
| + | real eps=10.^(-10); | ||
| + | for (int k=0; k<m; ++k) { | ||
| + | draw ( polargraph( new real(real x) {return cos(m*x)^(1/m);}, -(pi/2m)+eps+k*2pi/m, (pi/2m)-eps+k*2pi/m ), | ||
| + | defaultpen+1.5 ); | ||
| + | draw ( -r*expi(-pi/2m+k*2pi/m)..r*expi(-pi/2m+k*2pi/m), dashed ); | ||
| + | draw ( -r*expi(pi/2m+k*2pi/m)..r*expi(pi/2m+k*2pi/m), dashed ); | ||
| + | } | ||
| + | label( "$m=4$", (0.58,0.02), fontsize(7pt) ); | ||
| + | |||
| + | real eps=10.^(-2); | ||
| + | for (int k=0; k<m; ++k) { | ||
| + | draw ( polargraph( new real(real x) {return cos(m*x)^(-1/m);}, -(pi/2m)+eps+k*2pi/m, (pi/2m)-eps+k*2pi/m ), | ||
| + | defaultpen+1.5 ); | ||
| + | } | ||
| + | label( "$m=-4$", (1.55,0.02), fontsize(7pt) ); | ||
| + | |||
| + | label( "sinusoidal spiral: $a=1$", (0,2.3) ); | ||
| + | draw ( unitcircle, dashed ); | ||
| + | </asy></center> | ||
==Power function== | ==Power function== | ||
Revision as of 19:44, 4 December 2014
Experiments
Note a fine distinction from Ada:
I guess, the reason is that there Asy generates pdf file (converted into png afterwards), and here something else (probably ps).
More.
Mysterious.
Sinusoidal spiral
Power function
Kolmogorov test
Golden ratio
Strangely, the figure in EoM is erroneous! ED=EB, not BD=EB.
[Calculus: ] the art of numbering and measuring exactly a thing whose existence cannot be conceived. (Voltaire, Letter XVII: On Infinites In Geometry, And Sir Isaac Newton's Chronology)
And what are these fluxions? The velocities of evanescent increments? They are neither finite quantities, nor quantities infinitely small, nor yet nothing. May we not call them ghosts of departed quantities? (Berkeley, The Analyst)
WARNING: Asirra, the cat and dog CAPTCHA, is closing permanently on October 6, 2014. Please contact this site's administrator and ask them to switch to a different CAPTCHA. Thank you!
Boris Tsirelson/sandbox2. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Boris_Tsirelson/sandbox2&oldid=35310